JERUSALEM — More than a decade after being run out of Gaza by Hamas, the Palestinian Authority on Wednesday took control of the enclave’s border crossings, the most tangible sign yet of progress in the deal to end a bitter schism between the groups and ease the territory’s suffocating isolation.

For years, as Hamas and Fatah, which dominates the Palestinian Authority, explored reconciliation, one of the major stumbling blocks was security at the crossings. So it was a significant moment when Hamas formally handed control to the authority at a morning ceremony at the Rafah passenger crossing on the Egyptian border.

The Palestinian and Egyptian national anthems were played. The crossing was festooned with large portraits of President Abdel Fattah el-Sisi of Egypt and the Palestinian Authority president, Mahmoud Abbas, who has not set foot in Gaza since Hamas took over there after routing his forces in 2007.

The Palestinian Authority is internationally recognized whereas Hamas, the Islamic militant group, is classified as a terrorist organization by Israel, the United States and much of the West. With Palestinian Authority oversight of the border crossings, Gaza’s two million residents are now hoping for a significant easing of the blockade that Israel and Egypt imposed citing security concerns, severely restricting the movement of people and goods.

In an immediate sign of relief, the Palestinian Authority announced that it was canceling the collection of what it called “illegal” taxes and fees from Gazans, a reference to the unofficial levies of millions of dollars a month that Hamas has been skimming from cross-border imports and smuggling networks.

Under the deal between the Palestinian rival factions, signed in October and brokered by Egypt, Hamas agreed to hand over day-to-day governing of Gaza to the Palestinian Authority as well as transfer control of the crossings. Effectively, the agreement was an acknowledgment by Hamas, which has fought Israel three times, that it cannot govern Gaza without its rival.

The next steps in the deal are supposed to be a meeting this month in Cairo of all Palestinian factions, and talks aimed at a unity government.

But the agreement still leaves major issues unresolved. Chief among them is the fate of the formidable arsenal of rockets and fortified tunnels belonging to Hamas and other militant groups in Gaza, along with tens of thousands of fighters.

The Rafah crossing, which has opened only intermittently and for a few days at a time in recent years, is scheduled to become fully operational on Nov. 15, after Egypt finishes renovations on its side of the border. The Erez and Kerem Shalom crossings along the border with Israel, used mainly for humanitarian purposes, are expected to keep running.

“Opening the Rafah crossing is the biggest accomplishment for the Palestinian people and a historic gain,” said Fares Nasr, 60, an unemployed bus driver in Gaza City.

He said he has been unable to get to Egypt for medical treatment, and his daughter, who lives in Dubai, has been unable to visit Gaza and see her two sons studying at university there for five years.

Abu Khaled Hamdan, 60, another Gaza City resident, said he used to bring his son, who was studying engineering in Egypt, back for visits through a tunnel at a cost of $200 a trip.

The celebrations were tempered by a flare-up along the border with Israel this week, underscoring the fragility of the reconciliation. On Monday, Israel bombed what it said was an offensive tunnel belonging to Islamic Jihad that ran beneath the border fence into Israel. Israel said the bombing took place on its side of the fence, and the military said it was intended to disable the tunnel, not to kill senior militants.

Still, it turned into the deadliest cross-border event since the Gaza war of 2014. Five Islamic Jihad militants died, including two senior commanders. Two Hamas militants were also killed while carrying out what the group called a rescue mission.

Islamic Jihad is not a party to the reconciliation deal and the episode threatened to derail the fledgling unity accord. At least a half-dozen previous efforts at reconciliation between Hamas and Fatah, Mr. Abbas’s mainstream party, have failed.

But under pressure from Egypt, the groups did not immediately retaliate, allowing the ceremonies at the crossings to go ahead even as the search continued for more bodies.

Khaled al-Batsh, the leader of Islamic Jihad in Gaza, said after the attack, “Israel has tried to impose a new equation on the resistance, whereby Israel is allowed to kill, assassinate and raid whenever it wants.” Speaking at the hospital that was treating the wounded, he added, “We need to prevent it from doing so.”

Nonetheless, the Palestinian Authority prime minister, Rami Hamdallah, celebrated Wednesday’s events, saying his government’s assumption of responsibility at the crossings was “a pivotal step to empower the government and realize our national unity.”

The United Nations special coordinator for the Middle East peace process, Nickolay Mladenov, hailed it as a “landmark development” that “should facilitate the lifting of the closures, while addressing Israel’s legitimate security concerns, and unlock increased international support for Gaza’s reconstruction, growth, stability and prosperity.”

Israel, which has expressed strong reservations about any reconciliation deal that does not disarm Hamas, responded more cautiously. Gen. Yoav Mordechai, who leads Cogat, the Israeli government agency that coordinates with the Palestinian Authority on civil matters, instructed his staff to meet with Palestinian counterparts to work out joint work and security procedures at the crossings.

General Mordechai said Israel would insist on there being no Hamas personnel, or anyone working on the group’s behalf, involved in operating the crossings or in the vicinity of the crossings, according to a statement from his office.

Hamas seems determined to shed the burden of governing Gaza, but without accepting the Palestinian-Israeli agreements of the 1990s that gave rise to the Palestinian Authority, or forfeiting what it calls its “weapons of resistance” against Israel.

“The division is behind us,” Ismail Haniya, the leader of Hamas, said in a speech in Gaza on Wednesday, “and the reconciliation decision is irreversible.” He added, “We have completed the first stage of the reconciliation. Hamas has its own strategy for not recognizing Israel.”

Illustrating the deep and abiding differences between the rival Palestinian factions, Hamas accused Israel of crimes in the aftermath of the tunnel bombing and said Israel was deliberately trying to foil the reconciliation effort. Mr. Haniya also called on the Palestinian Authority to stop its security cooperation with Israel, a bedrock of the agreements between the two, which he described as a “flaw.”